Some additive operational laws of binary connection numbers are defined, and several new arithmetic aggregation operators, such as the binary connection number weighted arithmetic averaging(BCNWAA) operator, the binary connection number ordered weighted averaging(BCNOWA) operator and the binary connection number hybrid aggregation(BCNHA) operator, are proposed. Then an approach is developed for solving multiple criterion group decision making based on binary connection numbers with incomplete uncertain information. In this method, binary connection number criterion values are aggregated using the BCNWAA operator and the BCNHA operator, some optimal models are constructed to determine the optimal criterion weights using the variance of binary connection number criterion values and the randomness of criterion
weights. Finally, an example is given to illustrate the feasibility and effectiveness of the developed method.